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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Base-invariance implies Benford’s law
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by Theodore P. Hill PDF
Proc. Amer. Math. Soc. 123 (1995), 887-895 Request permission

Abstract:

A derivation of Benford’s Law or the First-Digit Phenomenon is given assuming only base-invariance of the underlying law. The only base-invariant distributions are shown to be convex combinations of two extremal probabilities, one corresponding to point mass and the other a log-Lebesgue measure. The main tools in the proof are identification of an appropriate mantissa $\sigma$-algebra on the positive reals, and results for invariant measures on the circle.
References
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 887-895
  • MSC: Primary 60A10; Secondary 28D05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1233974-8
  • MathSciNet review: 1233974